Porosity in the context of hypergroups


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Authors

  • Seyyed Mohammad Tabatabaie
  • Ali Reza Bagheri Salec
  • Haneen Ridha Jameel Allami

Keywords:

locally compact hypergroup, center of hypergroups, porosity, σ-lower porosity, spaceability, Lebesgue spaces, Hilbert spaces, convolution

Abstract

In this paper we show that the set of all elements mceclip0-9ecc89fe11547202e43f2dae25055a90.png for which mceclip1-73a4c33db2aeeeb08c81281807a7efc7.png for a center element mceclip2-8eaff47e98b28cf294da2548652f92a4.png, is mceclip3-cc230cb5e35cf62ceb70870dfdbb8ec4.png-c-lower porous, where mceclip4-668d692a9893bc1d28c982734ad1501b.png is a non-compact unimodular hypergroup and B is some special symmetric compact neighborhood of the identity element. As an application, we give some new equivalent condition for the finiteness of a discrete Hermitian hypergroup. Moreover, we give some sufficient conditions for the set of all pairs mceclip5.png in mceclip6.png for which for a center element mceclip7.png, is a mceclip3-cc230cb5e35cf62ceb70870dfdbb8ec4.png-c-lower porous, where mceclip8.png with mceclip9.png. Also, we show that the complement of this set is spaceable in mceclip10.png.

 

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Published

2024-04-08

How to Cite

Tabatabaie, S. M., Salec, A. R. B., & Allami, H. R. J. (2024). Porosity in the context of hypergroups. Eurasian Mathematical Journal, 15(1). Retrieved from https://emj.enu.kz/index.php/main/article/view/14

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